A digital twin of the subsurface is crucial for all performance and risks assessments of a CO2 storage activities. The goal of the project is to develop an efficient fully-coupled geomechanical simulator for CO2 storage capable to model fluid flow along cracks and faults and their associated opening and slip. To reach this goal, we extend the open-source finite element library Akantu to simulate the time-dependent hydro-mechanical changes associated with CO2 injection. Thanks to the high-performance computing capabilities of Akantu, the solver will allow representing the complete three-dimensional geological structure of a site including the presence of natural fractures and faults whose reactivation potential is critical to assess.